Metrics for bug329 (missed optimization)

analyze7.0ms (0.3%)

Memory

12.9MiB live, 12.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
0%	0%	50%	50%	0%	0%	0%	1
50%	25%	25%	50%	0%	0%	0%	2
50%	25%	25%	50%	0%	0%	0%	3
75%	37.5%	12.5%	50%	0%	0%	0%	4
75%	37.5%	12.5%	50%	0%	0%	0%	5
87.5%	43.7%	6.2%	50%	0%	0%	0%	6
87.5%	43.7%	6.2%	50%	0%	0%	0%	7
93.8%	46.8%	3.1%	50%	0%	0%	0%	8
93.8%	46.8%	3.1%	50%	0%	0%	0%	9
96.9%	48.4%	1.6%	50%	0%	0%	0%	10
96.9%	48.4%	1.6%	50%	0%	0%	0%	11
98.4%	49.2%	0.8%	50%	0%	0%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample516.0ms (22.6%)

Memory

50.7MiB live, 783.2MiB allocated

Samples

352.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 152.0ms

ival-div: 68.0ms (44.8% of total)

ival-atan: 50.0ms (32.9% of total)

ival->=: 24.0ms (15.8% of total)

exact: 7.0ms (4.6% of total)

ival-assert: 3.0ms (2% of total)

Bogosity

preprocess15.0ms (0.6%)

Memory

-14.4MiB live, 22.8MiB allocated

Algorithm

2×	egg-herbie

Rules

30×	`sub-neg`
20×	`+-commutative`
14×	`div-sub`
10×	`*-commutative`
10×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	25	30
2	37	30
3	47	30
4	55	30
5	69	30
6	89	30
7	99	30
8	101	30
0	4	4
0	4	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(atan (/ y x))

Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))

Call 2

Inputs
(atan (/ y x))
(atan (/ y (neg x)))
(atan (/ (neg y) x))
(neg (atan (/ y (neg x))))
(neg (atan (/ (neg y) x)))
(atan (/ x y))

Outputs
(atan (/ y x))
(atan (/ y (neg x)))
(atan (/ (neg y) x))
(atan (/ y (neg x)))
(neg (atan (/ y (neg x))))
(neg (atan (/ (neg y) x)))
(neg (atan (/ y (neg x))))
(atan (/ x y))

explain50.0ms (2.2%)

Memory

-19.6MiB live, 79.0MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f64 y x)`
-	-	`y`
-	-	`(atan.f64 (/.f64 y x))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

26.0ms

512×

valid

Compiler

Compiled 34 to 20 computations (41.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (52% of total)

ival-atan: 3.0ms (39% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(atan.f64 (/.f64 y x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 y x)
✓	cost-diff	0	(atan.f64 (/.f64 y x))

Rules

2×	`atan-lowering-atan.f32`
2×	`atan-lowering-atan.f64`
2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	4	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(atan (/ y x))
(/ y x)
y
x

Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))
(/ y x)
(/.f64 y x)
y
x

localize16.0ms (0.7%)

Memory

-11.9MiB live, 26.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 y x)
✓	accuracy	100.0%	(atan.f64 (/.f64 y x))

Samples

11.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (53.6% of total)

ival-atan: 1.0ms (26.8% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (atan (/ y x))>
#<alt (/ y x)>

Outputs
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(/ y x)
1.0ms	x	@	inf	(/ y x)
0.0ms	y	@	-inf	(/ y x)
0.0ms	y	@	0	(/ y x)
0.0ms	x	@	0	(/ y x)

rewrite66.0ms (2.9%)

Memory

12.8MiB live, 89.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

522×	`-lowering-.f32`
522×	`-lowering-.f64`
470×	`/-lowering-/.f32`
470×	`/-lowering-/.f64`
136×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	12	7
2	47	7
3	220	7
0	1218	7

Stop Event

1×	iter limit
1×	iter limit
1×	node limit

Counts

2 → 62

Calls

Call 1

Inputs
(atan (/ y x))
(/ y x)

Outputs
(-.f64 #s(literal 0 binary64) (atan.f64 (/.f64 y (neg.f64 x))))
(atan.f64 (/.f64 y x))
(neg.f64 (atan.f64 (/.f64 y (neg.f64 x))))
(*.f64 #s(literal -1 binary64) (atan.f64 (/.f64 y (neg.f64 x))))
(+.f64 #s(literal 0 binary64) (/.f64 y x))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64)) (/.f64 y x))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 x y))))
(-.f64 #s(literal 0 binary64) (/.f64 y (neg.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64) (/.f64 y x))
(neg.f64 (/.f64 y (neg.f64 x)))
(/.f64 y x)
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -1 binary64) (/.f64 x (neg.f64 y)))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 (/.f64 y (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 (neg.f64 x) (.f64 y y)))
(/.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) y))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) y)) (.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) (neg.f64 y))) (.f64 (neg.f64 x) x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x (neg.f64 y))) (neg.f64 x)) (.f64 (neg.f64 x) (/.f64 x (neg.f64 y))))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal 1 binary64)) (.f64 (*.f64 y y) (neg.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal -1 binary64)) (.f64 (*.f64 y y) x))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal 1 binary64)) (*.f64 y (neg.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal -1 binary64)) (*.f64 y x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 y (.f64 y y)))) (.f64 (neg.f64 x) (*.f64 y y)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 y y))) (*.f64 (neg.f64 x) y))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (.f64 y (.f64 y y)))) (.f64 x (*.f64 y y)))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (.f64 y y))) (*.f64 x y))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 y (neg.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (/.f64 y (neg.f64 x)) (/.f64 y (neg.f64 x)) (*.f64 #s(literal 0 binary64) (/.f64 y (neg.f64 x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 y (neg.f64 x)) (/.f64 y (neg.f64 x)))) (/.f64 y (neg.f64 x)))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (.f64 y (.f64 y y)))) (.f64 y y))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (.f64 y y))) y)
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal -1 binary64) x)) (.f64 y y))
(/.f64 (.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal -1 binary64) x)) y)
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 x y))) #s(literal -1 binary64))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 #s(literal -1 binary64) (/.f64 y (neg.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(*.f64 (/.f64 y (neg.f64 x)) #s(literal -1 binary64))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64))) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)))
(.f64 (/.f64 (neg.f64 y) (neg.f64 (.f64 x (.f64 x x)))) (.f64 x x))
(.f64 (/.f64 (neg.f64 y) (neg.f64 (.f64 x x))) x)

simplify33.0ms (1.5%)

Memory

-29.4MiB live, 11.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`atan-lowering-atan.f32`
2×	`atan-lowering-atan.f64`
2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	168
0	4	168

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)

Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)

eval13.0ms (0.6%)

Memory: 23.2MiB live, 23.2MiB allocated
Compiler: Compiled 820 to 197 computations (76% saved)

prune24.0ms (1%)

Memory

-20.5MiB live, 17.5MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	108	3	111

Accuracy

100.0%

Counts

111 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(atan.f64 (/.f64 y x))
▶	99.2%	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
▶	99.7%	(atan.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify5.0ms (0.2%)

Memory

6.7MiB live, 6.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 x y)
✓	cost-diff	0	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 x y))
✓	cost-diff	0	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(atan.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
✓	cost-diff	12864	(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
16×	`associate-r`
12×	`/-lowering-/.f32`
12×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	19	39
2	27	31
3	31	31
4	49	31
5	49	31
0	49	31

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(atan (* (pow x -1/2) (* (pow x -1/2) y)))
(* (pow x -1/2) (* (pow x -1/2) y))
(pow x -1/2)
x
-1/2
(* (pow x -1/2) y)
y
(atan (/ 1 (/ x y)))
(/ 1 (/ x y))
1
(/ x y)
x
y

Outputs
(atan (* (pow x -1/2) (* (pow x -1/2) y)))
(atan.f64 (/.f64 y x))
(* (pow x -1/2) (* (pow x -1/2) y))
(/.f64 y x)
(pow x -1/2)
(pow.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(* (pow x -1/2) y)
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
y
(atan (/ 1 (/ x y)))
(atan.f64 (/.f64 y x))
(/ 1 (/ x y))
(/.f64 y x)
1
#s(literal 1 binary64)
(/ x y)
(/.f64 x y)
x
y

localize42.0ms (1.8%)

Memory

5.9MiB live, 79.9MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x y)
✓	accuracy	100.0%	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 x y))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(atan.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
✓	accuracy	99.7%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
✓	accuracy	99.6%	(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))

Samples

27.0ms

256×

valid

Compiler

Compiled 49 to 13 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-pow: 6.0ms (33.3% of total)

ival-mult: 5.0ms (27.8% of total)

ival-div: 3.0ms (16.7% of total)

ival-atan: 3.0ms (16.7% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series10.0ms (0.4%)

Memory

21.7MiB live, 21.7MiB allocated

Counts

7 → 156

Calls

Call 1

Inputs
#<alt (* (pow x -1/2) (* (pow x -1/2) y))>
#<alt (atan (* (pow x -1/2) (* (pow x -1/2) y)))>
#<alt (pow x -1/2)>
#<alt (* (pow x -1/2) y)>
#<alt (/ 1 (/ x y))>
#<alt (atan (/ 1 (/ x y)))>
#<alt (/ x y)>

Outputs
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>
#<alt (/ x y)>

Calls

39 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(* (pow x -1/2) (* (pow x -1/2) y))
1.0ms	y	@	0	(/ x y)
1.0ms	x	@	0	(pow x -1/2)
1.0ms	y	@	0	(* (pow x -1/2) y)
0.0ms	x	@	-inf	(* (pow x -1/2) y)

rewrite309.0ms (13.5%)

Memory

-9.0MiB live, 515.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 328×	`accelerator-lowering-fma.f32`
3 328×	`accelerator-lowering-fma.f64`
3 202×	`-lowering-.f32`
3 202×	`-lowering-.f64`
1 960×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	42	25
2	153	25
3	749	25
4	5679	25
0	8110	25

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 657

Calls

Call 1

Inputs
(* (pow x -1/2) (* (pow x -1/2) y))
(atan (* (pow x -1/2) (* (pow x -1/2) y)))
(pow x -1/2)
(* (pow x -1/2) y)
(/ 1 (/ x y))
(atan (/ 1 (/ x y)))
(/ x y)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 y x))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64)) (/.f64 y x))
(exp.f64 (log.f64 (/.f64 y x)))
(exp.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (/.f64 x y))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (/.f64 x y))) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 y (neg.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64) (/.f64 y x))
(neg.f64 (/.f64 y (neg.f64 x)))
(/.f64 x (*.f64 (neg.f64 x) (/.f64 x (neg.f64 y))))
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y))
(/.f64 y x)
(/.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 #s(literal -1 binary64) (/.f64 x (neg.f64 y)))
(/.f64 (neg.f64 x) (*.f64 (neg.f64 x) (/.f64 x y)))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (pow.f64 x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 y (pow.f64 x #s(literal -3/4 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 y (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (/.f64 y x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))))
(/.f64 (*.f64 y (pow.f64 x #s(literal -3/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 (neg.f64 x) (.f64 y y)))
(/.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) y))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) y)) (.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) (neg.f64 y))) (.f64 (neg.f64 x) x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) x))) (/.f64 x y))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (/.f64 y (neg.f64 x)))) (neg.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) x))) (/.f64 x (neg.f64 y)))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal 1 binary64)) (.f64 (*.f64 y y) (neg.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal -1 binary64)) (.f64 (*.f64 y y) x))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal 1 binary64)) (*.f64 y (neg.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal -1 binary64)) (*.f64 y x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 y (.f64 y y)))) (.f64 (neg.f64 x) (*.f64 y y)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 y y))) (*.f64 (neg.f64 x) y))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (.f64 y (.f64 y y)))) (.f64 x (*.f64 y y)))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (.f64 y y))) (*.f64 x y))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (.f64 y (.f64 y y)))) (.f64 #s(literal -1 binary64) (*.f64 y y)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (.f64 y y))) (neg.f64 y))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal -1/2 binary64))) (pow.f64 y #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 y (neg.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (/.f64 y (neg.f64 x)) (/.f64 y (neg.f64 x)) (*.f64 #s(literal 0 binary64) (/.f64 y (neg.f64 x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 y (neg.f64 x)) (/.f64 y (neg.f64 x)))) (/.f64 y (neg.f64 x)))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (.f64 y (.f64 y y)))) (.f64 y y))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (.f64 y y))) y)
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal -1 binary64) x)) (.f64 y y))
(/.f64 (.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal -1 binary64) x)) y)
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 y x)) #s(literal 2 binary64))
(pow.f64 (/.f64 (.f64 x x) (.f64 y y)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 y x) (/.f64 y x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 x y)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)) #s(literal -1 binary64)))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (neg.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64)))))
(.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) (*.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 #s(literal -1 binary64) (/.f64 y (neg.f64 x)))
(*.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x))
(*.f64 (neg.f64 y) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 y (pow.f64 x #s(literal -3/4 binary64))))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (neg.f64 (*.f64 y (pow.f64 x #s(literal -3/4 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 (/.f64 y (neg.f64 x)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (/.f64 y x)) (sqrt.f64 (/.f64 y x)))
(*.f64 (sqrt.f64 (/.f64 y x)) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 y x)))))
(.f64 (sqrt.f64 (/.f64 y x)) (.f64 (neg.f64 (sqrt.f64 (/.f64 y x))) #s(literal -1 binary64)))
(.f64 (pow.f64 x #s(literal -1/8 binary64)) (.f64 y (pow.f64 x #s(literal -7/8 binary64))))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (/.f64 (pow.f64 x #s(literal -7/8 binary64)) (/.f64 #s(literal 1 binary64) y)))
(.f64 (pow.f64 x #s(literal -1/8 binary64)) (.f64 (*.f64 y (pow.f64 x #s(literal -7/8 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal -1/8 binary64)) (/.f64 (.f64 y (pow.f64 x #s(literal -7/8 binary64))) #s(literal 1 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64))) (neg.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64)))))
(.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64))) (*.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -3/4 binary64)))
(.f64 (pow.f64 x #s(literal -3/4 binary64)) (.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
(.f64 (pow.f64 y #s(literal 1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 y x))))
(*.f64 (pow.f64 y #s(literal 1/2 binary64)) (/.f64 (pow.f64 y #s(literal 1/2 binary64)) x))
(.f64 (pow.f64 y #s(literal 1/2 binary64)) (.f64 (pow.f64 y #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (neg.f64 x) #s(literal -1/2 binary64)) (.f64 (pow.f64 (neg.f64 y) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 y x))))
(.f64 (pow.f64 x #s(literal -1/16 binary64)) (.f64 (pow.f64 x #s(literal -1/16 binary64)) (*.f64 y (pow.f64 x #s(literal -7/8 binary64)))))
(.f64 (pow.f64 (/.f64 x y) #s(literal -1/4 binary64)) (.f64 (pow.f64 (/.f64 x y) #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 y x))))
(.f64 (pow.f64 x #s(literal -3/8 binary64)) (.f64 y (pow.f64 x #s(literal -5/8 binary64))))
(.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (neg.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y) #s(literal -1 binary64)))
(.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) #s(literal -1 binary64)))
(.f64 (neg.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)) (neg.f64 (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (neg.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (neg.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64)))))
(.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (.f64 (*.f64 y (pow.f64 x #s(literal -3/4 binary64))) #s(literal -1 binary64)))
(.f64 (neg.f64 (pow.f64 x #s(literal -1/4 binary64))) (/.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 y x))) (neg.f64 (sqrt.f64 (/.f64 y x))))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 y x))) (/.f64 (sqrt.f64 (/.f64 y x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))))
(.f64 (neg.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(.f64 (neg.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 x #s(literal -5/8 binary64)) (.f64 y (pow.f64 x #s(literal -3/8 binary64))))
(.f64 (.f64 y (pow.f64 x #s(literal -5/8 binary64))) (pow.f64 x #s(literal -3/8 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -3/8 binary64))) (pow.f64 x #s(literal -5/8 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -7/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -7/8 binary64))) (/.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -7/8 binary64))) (*.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal -7/8 binary64)) (.f64 y (pow.f64 x #s(literal -1/8 binary64))))
(.f64 (pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 y (pow.f64 x #s(literal -7/8 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) y) #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)) (neg.f64 y))
(.f64 (pow.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64))) #s(literal 1 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (pow.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 y (pow.f64 x #s(literal -7/8 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 1 binary64)))
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(/.f64 (.f64 (neg.f64 (/.f64 (.f64 x x) (*.f64 y y))) #s(literal -1 binary64)) (/.f64 x y))
(/.f64 (.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(/.f64 (.f64 (/.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/2 binary64))) y) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 y (pow.f64 x #s(literal -3/4 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 y x))) #s(literal -1 binary64)) (sqrt.f64 (/.f64 y x)))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(/.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal -1/4 binary64))) (*.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(/.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal -1/8 binary64))) (*.f64 y (pow.f64 x #s(literal -3/8 binary64))))
(/.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) (*.f64 y (pow.f64 x #s(literal -3/8 binary64)))) (pow.f64 x #s(literal -1/8 binary64)))
(/.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -3/8 binary64)))
(/.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) (pow.f64 x #s(literal -3/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(/.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(/.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) y) (pow.f64 x #s(literal -3/4 binary64)))
(/.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/8 binary64))) (*.f64 y (pow.f64 x #s(literal -5/8 binary64))))
(/.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 y (pow.f64 x #s(literal -5/8 binary64)))) (pow.f64 x #s(literal -1/8 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 y #s(literal 1/2 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) (pow.f64 y #s(literal 1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) (pow.f64 (neg.f64 x) #s(literal -1/2 binary64))) (pow.f64 (neg.f64 y) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) (pow.f64 (/.f64 x y) #s(literal -1/4 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/4 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (pow.f64 x #s(literal -3/4 binary64)))) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(pow.f64 (/.f64 x y) #s(literal 1 binary64))
(pow.f64 (/.f64 y x) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 y x)) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) #s(literal 2 binary64))
(pow.f64 (/.f64 (.f64 x x) (.f64 y y)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (/.f64 y x) (/.f64 y x)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 y x)))
(*.f64 x (/.f64 #s(literal 1 binary64) y))
(*.f64 #s(literal 1 binary64) (/.f64 x y))
(*.f64 (/.f64 x y) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 x (neg.f64 y)))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) y))
(*.f64 (neg.f64 x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)))
(*.f64 (/.f64 x (neg.f64 y)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) y) x)
(*.f64 (/.f64 #s(literal -1 binary64) y) (neg.f64 x))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) (pow.f64 x #s(literal 1/2 binary64)))
(.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) (.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) (/.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (pow.f64 x #s(literal -3/4 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 y #s(literal -1/2 binary64)) (.f64 (pow.f64 y #s(literal -1/2 binary64)) x))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/2 binary64))) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/2 binary64))) y))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 y (pow.f64 x #s(literal -3/4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -7/8 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/8 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -7/8 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal 1 binary64)) (neg.f64 x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 1/2 binary64)) y) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -3/4 binary64)))) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 y x))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -7/8 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (exp.f64 (log.f64 (neg.f64 x))) (exp.f64 (neg.f64 (log.f64 (neg.f64 y)))))
(*.f64 (/.f64 x (pow.f64 y #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 1/2 binary64))) (/.f64 (neg.f64 x) (pow.f64 y #s(literal 1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 y (pow.f64 x #s(literal -1/4 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -7/8 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/8 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) y) (pow.f64 x #s(literal -7/8 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -7/8 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -3/4 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) y) (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -7/8 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) y) (pow.f64 x #s(literal -1/8 binary64))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 x #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -7/8 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/2 binary64))) (/.f64 x (pow.f64 y #s(literal 1/2 binary64))))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/4 binary64))) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -3/4 binary64))))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -3/4 binary64))) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/8 binary64))) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -7/8 binary64))))
(*.f64 (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -7/8 binary64))) (/.f64 (pow.f64 y #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/8 binary64))))
(.f64 (.f64 x (pow.f64 y #s(literal -1/2 binary64))) (pow.f64 y #s(literal -1/2 binary64)))
(.f64 (/.f64 (neg.f64 x) (neg.f64 (.f64 y (.f64 y y)))) (.f64 y y))
(.f64 (/.f64 (neg.f64 x) (neg.f64 (.f64 y y))) y)

simplify145.0ms (6.3%)

Memory

-11.2MiB live, 102.0MiB allocated

Algorithm

1×	egg-herbie

Rules

1 124×	`div-sub`
824×	`associate-/r*`
736×	`-lowering-.f32`
736×	`-lowering-.f64`
736×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	640
1	33	616
2	69	608
3	155	608
4	583	608
5	1180	608
6	2140	608
7	2836	608
8	3452	608
9	4104	608
10	4540	608
11	4657	608
12	4733	608
13	4929	608
14	5113	608
15	5113	608
16	5113	608
17	5113	608
18	5113	608
0	5113	608

Stop Event

1×	iter limit
1×	saturated

Counts

156 → 156

Calls

Call 1

Inputs
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)
(/ x y)

Outputs
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)
(/ x y)
(/.f64 x y)

eval98.0ms (4.3%)

Memory: 14.0MiB live, 210.8MiB allocated
Compiler: Compiled 10 329 to 1 807 computations (82.5% saved)

prune69.0ms (3%)

Memory

1.7MiB live, 167.3MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	857	1	858
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	858	3	861

Accuracy

100.0%

Counts

861 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(atan.f64 (/.f64 y x))
✓	99.2%	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
▶	99.7%	(atan.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify4.0ms (0.2%)

Memory

8.1MiB live, 8.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
✓	cost-diff	(atan.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))

Rules

24×	`-lowering-.f32`
24×	`-lowering-.f64`
10×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	16	40
2	23	40
3	25	40
0	25	40

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(atan (* (sqrt (/ 1 x)) (* (pow x -1/2) y)))
(* (sqrt (/ 1 x)) (* (pow x -1/2) y))
(sqrt (/ 1 x))
(/ 1 x)
1
x
(* (pow x -1/2) y)
(pow x -1/2)
-1/2
y

Outputs
(atan (* (sqrt (/ 1 x)) (* (pow x -1/2) y)))
(atan.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(* (sqrt (/ 1 x)) (* (pow x -1/2) y))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* (pow x -1/2) y)
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
(pow x -1/2)
(pow.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
y

localize41.0ms (1.8%)

Memory

8.3MiB live, 79.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(atan.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) y)
✓	accuracy	99.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))

Samples

26.0ms

256×

valid

Compiler

Compiled 42 to 12 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow: 6.0ms (40.9% of total)

ival-mult: 3.0ms (20.5% of total)

ival-div: 2.0ms (13.6% of total)

ival-sqrt: 2.0ms (13.6% of total)

exact: 1.0ms (6.8% of total)

ival-atan: 1.0ms (6.8% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

5 → 96

Calls

Call 1

Inputs
#<alt (atan (* (sqrt (/ 1 x)) (* (pow x -1/2) y)))>
#<alt (* (sqrt (/ 1 x)) (* (pow x -1/2) y))>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (* (pow x -1/2) y)>

Outputs
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (* -1 (/ (* y (pow (sqrt -1) 2)) x))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(sqrt (/ 1 x))
0.0ms	x	@	-inf	(/ 1 x)
0.0ms	x	@	0	(atan (* (sqrt (/ 1 x)) (* (pow x -1/2) y)))
0.0ms	x	@	-inf	(atan (* (sqrt (/ 1 x)) (* (pow x -1/2) y)))
0.0ms	x	@	0	(/ 1 x)

rewrite64.0ms (2.8%)

Memory

-5.3MiB live, 83.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

338×	`-lowering-.f32`
338×	`-lowering-.f64`
164×	`/-lowering-/.f32`
164×	`/-lowering-/.f64`
98×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	37	22
2	119	17
0	548	17

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

5 → 142

Calls

Call 1

Inputs
(atan (* (sqrt (/ 1 x)) (* (pow x -1/2) y)))
(* (sqrt (/ 1 x)) (* (pow x -1/2) y))
(sqrt (/ 1 x))
(/ 1 x)
(* (pow x -1/2) y)

Outputs
(atan.f64 (/.f64 y x))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) y))
(neg.f64 (*.f64 y (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) (/.f64 y (sqrt.f64 x))))
(/.f64 y x)
(/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (neg.f64 (/.f64 y (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 y #s(literal 1 binary64)) x)
(/.f64 (*.f64 y #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) y) x)
(/.f64 (*.f64 (/.f64 y (sqrt.f64 x)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) y) (neg.f64 x))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 y (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 y (sqrt.f64 x))) (sqrt.f64 (neg.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 y (sqrt.f64 x)))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 y (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1 binary64) x) y))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (pow.f64 x #s(literal -1/4 binary64)) (/.f64 y (sqrt.f64 x))))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (*.f64 y (pow.f64 x #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (/.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) (sqrt.f64 x)))
(.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -3/4 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)))
(.f64 (pow.f64 x #s(literal -3/4 binary64)) (.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 y (pow.f64 x #s(literal -1/4 binary64)))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 y #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 y #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (.f64 y (pow.f64 x #s(literal -3/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 (/.f64 y (sqrt.f64 x)) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 x))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/4 binary64) (*.f64 (log.f64 x) #s(literal -1/4 binary64))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 x))))
(pow.f64 x #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 x))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 x))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 x))))
(.f64 (pow.f64 x #s(literal -1/8 binary64)) (.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -3/4 binary64))) (sqrt.f64 (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(exp.f64 (neg.f64 (log.f64 x)))
(exp.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 x) (*.f64 #s(literal -1/2 binary64) (log.f64 x))))
(exp.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 x) (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 x)))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 x)) (*.f64 #s(literal -1/2 binary64) (log.f64 x))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 x)) (*.f64 #s(literal 1/2 binary64) (neg.f64 (log.f64 x)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 x))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 x))))
(/.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (neg.f64 x))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 x)))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (sqrt.f64 (neg.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (neg.f64 x)))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (pow.f64 x #s(literal -3/4 binary64)) (.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(/.f64 y (sqrt.f64 x))
(/.f64 (*.f64 y #s(literal 1 binary64)) (sqrt.f64 x))
(/.f64 (*.f64 y #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 #s(literal 1 binary64) y) (sqrt.f64 x))
(/.f64 (*.f64 y (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 x)))
(/.f64 (*.f64 #s(literal -1 binary64) y) (neg.f64 (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) y) (sqrt.f64 (neg.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 y (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y)
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 y #s(literal 1 binary64)))
(*.f64 y (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1 binary64))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(.f64 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (*.f64 y (pow.f64 x #s(literal -1/4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 x #s(literal -1/8 binary64)) (.f64 (pow.f64 x #s(literal -1/8 binary64)) (*.f64 y (pow.f64 x #s(literal -1/4 binary64)))))
(.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 y (pow.f64 x #s(literal -1/4 binary64))) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 y #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(.f64 (.f64 (*.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/8 binary64))) (pow.f64 x #s(literal -1/8 binary64)))
(.f64 (.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (*.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 y (pow.f64 x #s(literal -1/4 binary64)))) (pow.f64 x #s(literal -1/4 binary64)))

simplify59.0ms (2.6%)

Memory

-9.2MiB live, 66.8MiB allocated

Algorithm

1×	egg-herbie

Rules

480×	`-lowering-.f32`
480×	`-lowering-.f64`
480×	`accelerator-lowering-fma.f32`
480×	`accelerator-lowering-fma.f64`
308×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	436
1	32	412
2	68	404
3	153	404
4	549	404
5	1090	404
6	1727	404
7	1789	404
8	1795	404
9	1795	404
0	1795	404

Stop Event

1×	iter limit
1×	saturated

Counts

96 → 96

Calls

Call 1

Inputs
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)

Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ (* y (pow (sqrt -1) 2)) x)))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(* -1 (/ (* y (pow (sqrt -1) 2)) x))
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(*.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

eval41.0ms (1.8%)

Memory: 5.4MiB live, 43.3MiB allocated
Compiler: Compiled 2 669 to 555 computations (79.2% saved)

prune21.0ms (0.9%)

Memory

-9.1MiB live, 34.8MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	238	3	241

Accuracy

100.0%

Counts

241 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(atan.f64 (/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x)))
✓	100.0%	(atan.f64 (/.f64 y x))
✓	99.2%	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify3.0ms (0.2%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 y (sqrt.f64 x))
✓	cost-diff	0	(atan.f64 (/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x)))
✓	cost-diff	1984	(/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x))

Rules

6×	`/-lowering-/.f32`
6×	`/-lowering-/.f64`
2×	`atan-lowering-atan.f32`
2×	`atan-lowering-atan.f64`
2×	`associate-/l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	23
1	8	15
2	9	15
3	10	15
0	10	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(atan (/ (/ y (sqrt x)) (sqrt x)))
(/ (/ y (sqrt x)) (sqrt x))
(/ y (sqrt x))
y
(sqrt x)
x

Outputs
(atan (/ (/ y (sqrt x)) (sqrt x)))
(atan.f64 (/.f64 y x))
(/ (/ y (sqrt x)) (sqrt x))
(/.f64 y x)
(/ y (sqrt x))
(/.f64 y (sqrt.f64 x))
y
(sqrt x)
(sqrt.f64 x)
x

localize24.0ms (1.1%)

Memory

-0.6MiB live, 37.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(atan.f64 (/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x)))
✓	accuracy	99.6%	(/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 y (sqrt.f64 x))

Samples

13.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 3.0ms (44.3% of total)

ival-sqrt: 2.0ms (29.6% of total)

ival-atan: 1.0ms (14.8% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (/ (/ y (sqrt x)) (sqrt x))>
#<alt (atan (/ (/ y (sqrt x)) (sqrt x)))>
#<alt (/ y (sqrt x))>
#<alt (sqrt x)>

Outputs
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (* -1 (/ y (* x (pow (sqrt -1) 2))))>
#<alt (* -1 (/ y (* x (pow (sqrt -1) 2))))>
#<alt (* -1 (/ y (* x (pow (sqrt -1) 2))))>
#<alt (* -1 (/ y (* x (pow (sqrt -1) 2))))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))>
#<alt (atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))>
#<alt (atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))>
#<alt (atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ y (sqrt x))
0.0ms	x	@	-inf	(/ (/ y (sqrt x)) (sqrt x))
0.0ms	x	@	-inf	(sqrt x)
0.0ms	x	@	-inf	(atan (/ (/ y (sqrt x)) (sqrt x)))
0.0ms	y	@	0	(/ (/ y (sqrt x)) (sqrt x))

rewrite171.0ms (7.5%)

Memory

-23.3MiB live, 261.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 224×	`-lowering-.f32`
2 224×	`-lowering-.f64`
1 982×	`accelerator-lowering-fma.f32`
1 982×	`accelerator-lowering-fma.f64`
1 230×	`log-div`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	21
1	23	13
2	130	13
3	767	13
4	4962	13
0	8619	13

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 418

Calls

Call 1

Inputs
(/ (/ y (sqrt x)) (sqrt x))
(atan (/ (/ y (sqrt x)) (sqrt x)))
(/ y (sqrt x))
(sqrt x)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 y x))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) (/.f64 y x))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64)) (/.f64 y x))
(exp.f64 (log.f64 (/.f64 y x)))
(exp.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 x y) (/.f64 x y))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 y x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 x y)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 x y)) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 y x))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 0 binary64) (/.f64 y x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64) (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 y x)
(/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (neg.f64 y) x)
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) y))
(/.f64 #s(literal -1 binary64) (/.f64 x y))
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (/.f64 y x) #s(literal -1 binary64))
(/.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (*.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (*.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (sqrt.f64 x)))) (/.f64 (sqrt.f64 (sqrt.f64 x)) y))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 (sqrt.f64 (sqrt.f64 x)) y)))
(/.f64 (/.f64 y (sqrt.f64 (*.f64 x (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
(/.f64 (/.f64 y (sqrt.f64 (*.f64 x (sqrt.f64 x)))) (neg.f64 (sqrt.f64 (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 (*.f64 x (sqrt.f64 x))) y))
(/.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 x (sqrt.f64 x))) (.f64 (sqrt.f64 x) (/.f64 (*.f64 y y) x)))
(/.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 x (sqrt.f64 x))) (.f64 (/.f64 (*.f64 y y) x) (sqrt.f64 x)))
(/.f64 (/.f64 (.f64 y y) x) (.f64 (sqrt.f64 x) (/.f64 y (sqrt.f64 x))))
(/.f64 (/.f64 (.f64 y y) x) (.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 x (.f64 y y)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 (neg.f64 (.f64 y y)) (.f64 x y))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 (sqrt.f64 x) y)) (*.f64 x (sqrt.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 x) (/.f64 y (sqrt.f64 x)))) x)
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 (sqrt.f64 x) (neg.f64 y))) (*.f64 x (sqrt.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x y)) (sqrt.f64 x)) (.f64 (sqrt.f64 x) (/.f64 x y)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x))) (/.f64 (sqrt.f64 x) y))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 x) (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))))) (sqrt.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 x y))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 x y)) (*.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (/.f64 y (sqrt.f64 x)))) (.f64 x (sqrt.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 x (neg.f64 y))) (*.f64 x x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x y)) x) (.f64 x (/.f64 x y)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 (sqrt.f64 x))) (.f64 x (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))))) (.f64 x (sqrt.f64 (sqrt.f64 x))))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal 1 binary64)) (.f64 (*.f64 y y) x))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal -1 binary64)) (.f64 (*.f64 y y) x))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal 1 binary64)) (*.f64 y x))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal -1 binary64)) (*.f64 y x))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 (*.f64 x (sqrt.f64 x))) y))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) #s(literal -1 binary64)) (/.f64 (sqrt.f64 (.f64 x (sqrt.f64 x))) y))
(/.f64 (.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) #s(literal 1 binary64)) (sqrt.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) #s(literal -1 binary64)) (sqrt.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))) #s(literal 1 binary64)) (sqrt.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))) #s(literal -1 binary64)) (sqrt.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 x (sqrt.f64 x))) #s(literal -1 binary64)) (.f64 (/.f64 (.f64 y y) x) (sqrt.f64 x)))
(/.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x)))) (.f64 (/.f64 (.f64 y y) x) (sqrt.f64 (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 (.f64 y y) x) #s(literal -1 binary64)) (*.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (.f64 (/.f64 (.f64 y y) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x)))) (*.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 (*.f64 y y) (sqrt.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x))))) (.f64 (.f64 y y) (sqrt.f64 (sqrt.f64 x))))
(/.f64 (.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 y (sqrt.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x))))) (.f64 y (sqrt.f64 (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) y) (sqrt.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (neg.f64 y)) (sqrt.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (.f64 y (.f64 y y)) (.f64 x (sqrt.f64 x)))) (.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (.f64 y y) x)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (.f64 y y) x)) (*.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 y (sqrt.f64 x))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (neg.f64 (.f64 y (.f64 y y)))) (.f64 (sqrt.f64 x) (*.f64 y y)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (neg.f64 (.f64 y y))) (*.f64 (sqrt.f64 x) y))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 x y) #s(literal -3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (/.f64 y x) (/.f64 y x) (*.f64 #s(literal 0 binary64) (/.f64 y x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 y x) (/.f64 y x))) (/.f64 y x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 y (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(/.f64 (.f64 (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 x)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) y) (sqrt.f64 (sqrt.f64 x)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (.f64 y (.f64 y y)) (.f64 x (sqrt.f64 x)))) (/.f64 (*.f64 y y) x))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (.f64 y y) x)) (/.f64 y (sqrt.f64 x)))
(/.f64 (*.f64 (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (.f64 y (.f64 y y)))) (.f64 y y))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (.f64 y y))) y)
(/.f64 (.f64 (/.f64 (.f64 y (.f64 y y)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 (*.f64 y y) x))
(/.f64 (.f64 (/.f64 (.f64 y y) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 y (sqrt.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) x)) (.f64 y y))
(/.f64 (.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal 1 binary64) x)) y)
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) y)) x)
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) x)
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (sqrt.f64 x)) y)) (sqrt.f64 (*.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 (sqrt.f64 x)) y))) (sqrt.f64 (*.f64 x (sqrt.f64 x))))
(/.f64 (/.f64 (/.f64 y (sqrt.f64 (*.f64 x (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal -1/2 binary64))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 y (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 y (sqrt.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 y x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 (/.f64 y x) #s(literal -1 binary64))
(.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))))
(.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)))
(.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)))
(.f64 (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))))
(.f64 (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)))
(.f64 (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) (/.f64 y (sqrt.f64 (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) (/.f64 (neg.f64 y) (sqrt.f64 (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) (*.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) (/.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) #s(literal 1 binary64)))
(.f64 (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))))
(.f64 (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x))))
(.f64 (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x)))))
(.f64 (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 y (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (.f64 (/.f64 y (sqrt.f64 (*.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x (sqrt.f64 x)))) y))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 x) y)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) y)))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 y))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64)) (.f64 (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))))
(.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x)))) (/.f64 y (sqrt.f64 (.f64 x (sqrt.f64 x)))))
(*.f64 (neg.f64 (pow.f64 (/.f64 x y) #s(literal -1/2 binary64))) (pow.f64 (/.f64 x y) #s(literal -1/2 binary64)))
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(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x))) (.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x))) (/.f64 (/.f64 y (sqrt.f64 (sqrt.f64 x))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x)))) (/.f64 y (sqrt.f64 (sqrt.f64 x))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x)))) (/.f64 y (sqrt.f64 (sqrt.f64 x))))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64))) (pow.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x)))) (/.f64 y (sqrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) y)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(.f64 (/.f64 y (.f64 x (sqrt.f64 x))) x)
(.f64 (/.f64 (neg.f64 y) (.f64 x (sqrt.f64 x))) x)
(+.f64 (sqrt.f64 x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (sqrt.f64 x))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 x)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(fabs.f64 (sqrt.f64 x))
(fabs.f64 (-.f64 (sqrt.f64 x) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(sqrt.f64 x)
(fma.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 (*.f64 x (sqrt.f64 x))) (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (*.f64 x (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 3/4 binary64) (log.f64 x))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (*.f64 x (sqrt.f64 x))) (/.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (*.f64 x (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 3/4 binary64) (log.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64))) #s(literal 0 binary64))
(neg.f64 (sqrt.f64 x))
(/.f64 x (sqrt.f64 x))
(/.f64 (sqrt.f64 x) #s(literal 1 binary64))
(/.f64 (sqrt.f64 x) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 x (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))))
(/.f64 (*.f64 x (sqrt.f64 x)) x)
(/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 #s(literal 0 binary64) (-.f64 x #s(literal 0 binary64))))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 4 binary64))
(pow.f64 (.f64 (.f64 (*.f64 x x) x) x) #s(literal 1/8 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (sqrt.f64 x))) #s(literal -2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (*.f64 x x) x) x)) #s(literal 1/16 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(pow.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 x) x) #s(literal -1 binary64))
(pow.f64 (/.f64 x (*.f64 x (sqrt.f64 x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (sqrt.f64 x) #s(literal -1 binary64))
(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 #s(literal -1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x)))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (/.f64 (sqrt.f64 (.f64 x (sqrt.f64 x))) (sqrt.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 x)))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 (sqrt.f64 x)))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 3/4 binary64) (log.f64 x))))
(*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 x))) (/.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(.f64 (.f64 x (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 3/4 binary64) (log.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64))))

simplify126.0ms (5.5%)

Memory

4.6MiB live, 81.6MiB allocated

Algorithm

1×	egg-herbie

Rules

712×	`times-frac`
608×	`-lowering-.f32`
608×	`-lowering-.f64`
608×	`accelerator-lowering-fma.f32`
608×	`accelerator-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	336
1	34	336
2	94	336
3	186	336
4	558	336
5	1909	336
6	2527	336
7	2777	336
8	2901	336
9	2927	336
10	2946	336
11	3067	336
12	3354	336
13	3531	336
14	3683	336
15	3731	336
16	3731	336
17	3731	336
0	3731	336

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

Calls

Call 1

Inputs
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(/.f64 y x)
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(/.f64 y x)
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(/.f64 y x)
(* -1 (/ y (* x (pow (sqrt -1) 2))))
(/.f64 y x)
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(atan.f64 (/.f64 y x))
(atan (* -1 (/ y (* x (pow (sqrt -1) 2)))))
(atan.f64 (/.f64 y x))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) y)
(*.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

eval110.0ms (4.8%)

Memory: -5.9MiB live, 109.2MiB allocated
Compiler: Compiled 8 211 to 1 704 computations (79.2% saved)

prune122.0ms (5.4%)

Memory

12.0MiB live, 132.6MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	621	0	621
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	621	3	624

Accuracy

100.0%

Counts

624 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(atan.f64 (/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x)))
✓	100.0%	(atan.f64 (/.f64 y x))
✓	99.2%	(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))

Compiler

Compiled 65 to 37 computations (43.1% saved)

regimes9.0ms (0.4%)

Memory

15.6MiB live, 15.6MiB allocated

Accuracy

Total -0.7b remaining (-9019.9%)

Threshold costs -0.7b (-9019.9%)

Counts

5 → 1

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(atan.f64 (/.f64 #s(literal 1 binary64) (/.f64 x y)))
(atan.f64 (/.f64 (/.f64 y (sqrt.f64 x)) (sqrt.f64 x)))
(atan.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))
(atan.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y)))

Outputs
(atan.f64 (/.f64 y x))

Calls

4 calls:

2.0ms	y
2.0ms	x
2.0ms	(/.f64 y x)
2.0ms	(atan.f64 (/.f64 y x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(atan.f64 (/.f64 y x))`
100.0%	1	`(/.f64 y x)`

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify33.0ms (1.4%)

Memory

-24.9MiB live, 11.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4

Stop Event

1×

saturated

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))

Outputs
(atan.f64 (/.f64 y x))

soundness0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Stop Event

1×

done

Compiler

Compiled 6 to 4 computations (33.3% saved)

preprocess28.0ms (1.2%)

Memory: 30.3MiB live, 69.7MiB allocated
Compiler: Compiled 34 to 22 computations (35.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze7.0ms (0.3%)

sample516.0ms (22.6%)

preprocess15.0ms (0.6%)

explain50.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize16.0ms (0.7%)

series3.0ms (0.1%)

rewrite66.0ms (2.9%)

simplify33.0ms (1.5%)

eval13.0ms (0.6%)

prune24.0ms (1%)

simplify5.0ms (0.2%)

localize42.0ms (1.8%)

series10.0ms (0.4%)

rewrite309.0ms (13.5%)

simplify145.0ms (6.3%)

eval98.0ms (4.3%)

prune69.0ms (3%)

simplify4.0ms (0.2%)

localize41.0ms (1.8%)

series2.0ms (0.1%)

rewrite64.0ms (2.8%)

simplify59.0ms (2.6%)

eval41.0ms (1.8%)

prune21.0ms (0.9%)

simplify3.0ms (0.2%)

localize24.0ms (1.1%)

series3.0ms (0.1%)

rewrite171.0ms (7.5%)

simplify126.0ms (5.5%)

eval110.0ms (4.8%)

prune122.0ms (5.4%)

regimes9.0ms (0.4%)

simplify33.0ms (1.4%)

soundness0.0ms (0%)

preprocess28.0ms (1.2%)

end0.0ms (0%)

Profiling